By that time, however, the home crowd had been thrilled by the debut of Shunsuke Nakamura, who had shown some superb touches and awareness throughout the match. His substitution six minutes from time earned him a deserved standing ovation.
The Japanese player announced himself with a header in the first minute which was cleared off the line by Stuart Duff. He added poise to the Celtic midfield with his subtle touches.
Lee Miller latched on to a loose ball before seeing Jim McIntyre head his cross into the side netting in a rare attack from the visitors.
Artur Boruc, in the Celtic goal, looked less than commanding at crosses, and from a corner by Mark Wilson a scramble in the Celtic six-yard box ended with McIntyre heading tamely into the keeper's arms.
Maciej Zurawski squandered a superb chance when Nakamura's early pass put him through on goal, but Derek Stillie blocked the shot.
Celtic's pressure paid off when John Hartson out-muscled David McCracken before shooting low past Stillie.
In the second half Hartson twice watched headers come back off the cross bar and Stillie did well to claw away a Nakamura free kick.
Shaun Maloney, who had come on for the ineffective Maciej Zurawski, found Beattie with a delicate pass which the striker volleyed home superbly.